Of course they preferred the Typhoon. A single engined fighter with 2000BHP v a twin engined fighter with 1,600BHP. And eventually they were correct, the Sea Fury was the ultimate progression of the Typhoon/Tempest/Fury as up there with the best of piston engined fighters. Any theoretical progression of a peregrine twin fighter would be eaten by a Tempest or Fury.
I cannot think of an example of a twin fighter out performing a single in the front line. There is much debate here about the P 39 .....but in Europe it was not a success.
The Fury came too late to be useful in WWII and the Tempest itself was only useful late war. Compared to the P-38 (which I assume you meant rather than P-39) the Whirlwind had MANY fewer teething problems and with the level of support the P-38 got, would have been a highly competitive fighter far sooner than that American twin AND without the same issues of being much larger an dheavier than single engine counterparts or having poor roll response without boosted ailerons. (IMO the P-38 should have gotten spring tab boosted ailerons from the start like the F4U -no hydraulics needed- ... a stick might have offered better response and leverage than that yolk too)
Aisde from that you ALSO had Gloster's twin designs and Supermarines ones among others that went unexploited and left on paper while the Typhoon got forced along with poor high speed aerodynamics and a very troubled engine.
The Typhoon had NO engine in reliable mass production in 1940 ... or 1941, the Whirlwind did in 1939.
I'm also not talking about super powered Merlin or Peregrine engines, I'm talking about the existing 800~1100 hp class engines of 1939 (1310 hp WEP in the BoB -I'm sure higher on RR bench tests) that had SOME obvious potential for growth and at very least could be expected to maintain existing production quality. In 1939 the Peregrine was likely better off than the Taurus in reliability terms as well.
Banking on new, unproven engines is a massive risk that twin engine fighters consistently avoid using existing lower powered engines to achieve their performance.
The Sabre was retired as soon as the war ended but the Spitfire and the Griffon served for years after
The Griffon and Merlin deserved the most of RR's development attention for sure and an earlier Griffon would have been more useful than the Peregrine BUT there's still a great deal of engineering commonality between all three engines so it's not so clear if canceling any one earlier or developing one more aggressively earlier would have helped. The Vulture shared less in common design wise and would be a more rational design to drop early on.
It might have been good to compromise with a rationalized mass-production capable Rolls Royce R that omitted some of the refinements the Griffon targeted (including smaller frontal area) in favor of quicker time to production.
The Taurus was showing problems early on that had some commonalities with the Aquila, I believe, and some new problems on top of that while the Hercules was developing more smoothly and in a more useful power range, so even in 1939 and 1940 there was plenty of rational reason to kill the Taurus and focus on the Hercules.
The problems with the slats were only identified much later, after the type had been operational for some time. I imagine it was a case of pushing things a bit farther in combat than in initial testing.
For example, while testing the Whirlwind, the A&AEE listed a limiting dive speed of 420 mph IAS. The official Pilot's Notes list a maximum diving speed of 400 mph IAS.
The CO of 263 Squadron, however, said they had dived them to 460 mph IAS.
Had the Whirlwind been deployed more aggressively sooner, that should have been exposed sooner as well (enough to get worked into the Mk.II I'd think). As it stood, it might have made sense to use a locking mechanism that could be applied and removed depending on the mission profile. Fighter-bomber loads would seem more worth the risk for the improved take-off run, while fighter patrol and interception duties would make more sense to keep wired shut. (if they had more planes, having some wired shut and others left unlocked would probably be easier)
Now maybe the Peregrine was fatally flawed (or had multiple flaws) that prevented the use of even 9lb boost let alone 12lbs. Or maybe it needed a new crank, rods, crankcase, cylinder blocks,etc to get to 16-18lbs of boost. I have no idea.
But there is a world of difference between cruising at 7-10lbs of boost (running at 100 octane levels) 100% of the time and cruising at 2-4lbs boost and using the 7-12lbs boost for take-off and emergencies.
I suspect RR might have been using excessive caution with the Peregrine due to the very limited number of spares and spare parts, somewhat like was discussed for the V-1710 recently. (though more legitimately extreme)
Now before I get accused of saying Rolls Royce was lying, IF Rolls Royce was saying that in order to make 100% use of the potential of 100 octane fuel then they could very well have been right. To make full use of 100 octane would require the engine to operate at 16-18lbs of boost and would require quite possibly a new supercharger
The exact same thing is true of the V-1710 at the time, both the -39 and especially the older -33 (more contemporary with the Merlin III and Peregrine). They required 100/100 octane fuel, but ran pretty much entirely in envelopes 87 octane likely would have been fine with the possible exception of running extremely lean. (most 87 octane fuel was much closer to 87/100 than 87/87) American 100 octane was of course chemically very different from British mixtures with almost no aromatics and considerably less lead.
The -33 (C-15) ran at Military/Emergency power of under +4 psi boost (37"), though overboosting (which that official USAAC/Allison chart on Peril's site shows) clearly showed potential for going all out at sea level and pulling around 66" (+16.6 psi) and nearly 1700 hp at 3000 rpm without using ram. Detonation was not a limiting factor there, but engine structural integrity was. Allison warned that pulling max boost on the later F3R (39) and F4R (73) could destroy the engine (in reality I believe it was the F3R more seriously vulnerable and Allison was always a bit more cautious than Rolls Royce with both boost and limiting RPM).
I'd expect the Peregrine to be in a similar situation to the V-1710-33 and possibly similar in ability to use 100 octane fuel for leaner, more efficient cruise. To get a 1200 hp class engine out of the Peregrine, it's probably going to end up at nearly as heavy as the Merlin III. THAT might be a problem for the Whirlwind: if the peregrine saw the same weight creep as the Merlin, and it was truly as tight a design as some authors imply or claim, that would mean it would be more difficult to adapt to new engines than the Spitfire. (honestly, the Peregrine to Merlin III swap shouldn't have been much more trouble than the Merlin VII to XX swap for the Spit III let alone the Merlin 45 to 61 transition ... or the Griffon)
Still, it should at very least tolerate a Merlin III => Merlin 45 style engine performance upgrade optimized around minimal modifications like the Spit V was.